Jump risk and option liquidity in an incomplete market

This study investigates the effect of a jump risk on options’ bid–ask implied volatility (IMV) spreads. We introduce theoretical models assuming market makers encounter a Bernoulli‐type jump atnd optimize the mean‐variance utility by choosing the optimal hedging delta and price. We find, at a low jump arrival rate, the Black–Scholes–Merton dynamic hedging for diffusion volatility outperforms static hedging for both diffusion and jump risks. If dynamic hedging is implemented, the jump components nonlinearly affect bid–ask spreads. Our regression supports our theoretical conclusions, and for model‐free IMV, jump risk factors are characterized by t statistics above 7 with adjusted R 2 above 70%.